Course Description: Math 6510 is intended for
all graduate students in
mathematics. This course will be an introduction to algebraic number
theory and
some background in abstract algebra is required. We will discuss
algebraic
number fields and their basic properties such as ring of integers,
lattices,
prime factorizations, and class numbers. We will also investigate the
geometry
of algebraic numbers, congruences, p-adic numbers, and further topics
if time
permits.

Textbook:You
do not
have to
buy a textbook for this class, since we will not follow a particular
textbook
very closely. A large portion of the material that we will cover can be
found
for example in the following books: